Spin-orbit semimetals in the layer groups

Abstract

Recent interest in point and line node semimetals has led to the proposal and discovery of these phenomena in numerous systems. Frequently, though, these nodal systems are described in terms of individual properties reliant on specific space group intricacies or band-tuning conditions. Restricting ourselves to cases with strong spin-orbit interaction, we develop a general framework which captures existing systems and predicts new examples of nodal materials. In many previously proposed systems, the three-dimensional nature of the space group has obscured key generalities. Therefore, we show how within our framework one can predict and characterize a diverse set of nodal phenomena even in two-dimensional systems constructed of three-dimensional sites, known as the "Layer Groups". Expanding on an existing discussion by Watanabe, Po, Vishwanath, and Zaletel of the relationship between minimal insulating filling, nonsymmorphic symmetries, and compact flat manifolds, we characterize the allowed semimetallic structures in the layer groups and draw connections to related three-dimensional systems.

Topologically stable gapless phases in nonsymmorphic superconductors

“…Because of nonsymmorphic symmetry and strong SOC in SrIrO 3 , the line node is topologically protected 58 . Recently, versatile topological semimetals [59][60][61][62][63][64][65] and insulators 66? -78 with nontrivial influence of nonsymmorphic symmetry have been anticipated theoretically.…”

Interacting Weyl fermions: Phases, phase transitions, and global phase diagram

“…At one loop level, the correlation length exponent for continuous transitions is ν = n/2, indicating their non-Gaussian nature for any n > 1. We also discuss scaling of thermodynamic and transport quantities inside the broken symmetry phases.Introduction: There is tremendous ongoing interest in three dimensional, gapless topological systems [1][2][3][4][5][6]. An interesting class of such systems is described by the isolated nodal points of time reversal or inversion symmetry breaking materials, where two non-degenerate bands touch [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”

Data Mining for Three-Dimensional Organic Dirac Materials: Focus on Space Group 19

“…There is also a second opportunity of hosting Dirac crossing as accidental crossings 23 , which are protected by band topology. Such crossings can be found for instance in crystals with the monoclinic space group P 2 1 / c (#14) 6, 24 . In crystals with this space group, electronic energy bands are sticking together in groups of four bands.…”